Question: Simplify the following expression: $ p = \dfrac{q - 2}{q - 1} - \dfrac{-3}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{q - 2}{q - 1} \times \dfrac{7}{7} = \dfrac{7q - 14}{7q - 7} $ Multiply the second expression by $\dfrac{q - 1}{q - 1}$ $ \dfrac{-3}{7} \times \dfrac{q - 1}{q - 1} = \dfrac{-3q + 3}{7q - 7} $ Therefore $ p = \dfrac{7q - 14}{7q - 7} - \dfrac{-3q + 3}{7q - 7} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{7q - 14 - (-3q + 3) }{7q - 7} $ Distribute the negative sign: $p = \dfrac{7q - 14 + 3q - 3}{7q - 7}$ $p = \dfrac{10q - 17}{7q - 7}$